Pion-induced ${K}^{* }$ production with ${{\rm{\Sigma }}}^{* }$ baryon off proton target

In this work, the reaction ${\pi }^{-}p\to {K}^{* }{{\rm{\Sigma }}}^{* }$ is investigated with an effective Lagrangian approach. The contributions from the Born terms, including the s, t, and u channel, are considered, and the Regge model and the Feynman model are applied to treat the t -channel contribution. The existing experimental data can be reproduced with the best-fitted χ ² being 2.38 and 1.54 for the Feynman and Regge models, respectively. Moreover, it is found that the contribution from the t channel is dominant in the cross-section. The contribution of the u channel is mainly distributed at backward angles, and the contribution from the s channel is small and negligible. In the Feynman model, the contribution of the t -channel K exchange is much larger than the contribution of the ${K}^{* }$ exchange, while in the Regge model the contribution of the t -channel K exchange is comparable to that of the ${K}^{* }$ exchange. Prediction about the differential cross-section of the ${\pi }^{-}p\to {K}^{* }{{\rm{\Sigma }}}^{* }$ reaction is also presented, which is helpful for clarifying the role of the Regge treatment. The current results suggest high-precision experimental measurements which can be performed at J-PARC and COMPASS.     

Pure annihilation decays of B_s~0→a_0~+a_0~- and B_d~0→K_0~(*+)K_0~(*-) in the PQCD approach

We study the CP-averaged branching fractions and the CP-violating asymmetries in the pure annihilation decays ofB _s~0→a_0~+a _0~-andB _d~0→K_0~(*+)K_0~(*-),where a_0[K_0~*]denotes the scalar a_0(980) and a_0(1450)[K_0~*(800)(ork)and K_0~*(1430)],with the perturbative QCD factorization approach under the assumption of two-quark structure for the a_0and K_0~*states.The numerical results show that the branching ratios of theB _d~0→K_0~(*+)K_0~(*-)decays are in the order of 10~(-6),while the decay rates of theB_s~0→a_0~+a _0~-modes are in the order of 10~(-5).In light of the measured modes with the same quark components in the pseudoscalar sector,namely,B _d~0→K~+K~-and B_s~0→p p~(+-),the predictions for the considered decay modes in this work are expected to be measured at the Large Hadron Collider beauty and/or Belle-Ⅱ experiments in the (near) future.Meanwhile,it is of great interest to find that the twist-3 distribution amplitudes φ~S and φ~T with inclusion of the Gegenbauer polynomials for the scalar a_0(1450) and K_0~*(1430)states in scenario2 contribute slightly to the branching ratios while significantly to the CP violations in the B_d~0→K_0~*(14 30)~+K_0*(14 30)~-and B_s~0→a_0(1450)~+a_0(1450)~-decays,which indicates that,compared to the asymptotic φ~Sand φ~T,these Gegenbauer polynomials could change the strong phases evidently in these pure annihilation decay channels.These predictions await for the future confirmation experimentally,which could further provide useful information to help explore the inner structure of the scalars and shed light on the annihilation decay mechanism.     

${{ \mathcal H }}_{\infty }$ synchronization of chaotic Hopfield networks with time-varying delay: a resilient DOF control approach*

This paper focuses on the issue of resilient dynamic output-feedback (DOF) control for ${{ \mathcal H }}_{\infty }$ synchronization of chaotic Hopfield networks with time-varying delay. The aim is to determine a DOF controller with gain perturbations ensuring that the ${{ \mathcal H }}_{\infty }$ norm from the external disturbances to the synchronization error is less than or equal to a prescribed bound. A delay-dependent criterion for the ${{ \mathcal H }}_{\infty }$ synchronization is derived by employing the Lyapunov functional method together with some recent inequalities. Then, with the help of some decoupling techniques, sufficient conditions on the existence of the resilient DOF controller are developed for both the time-varying and constant time-delay cases. Lastly, an example is used to illustrate the applicability of the results obtained.     

Analysis of the Possible $D\bar{D}_{s0}^*(2317)$ and $D^*\bar{D}_{s1}^*(2460)$ Molecules with QCD Sum Rules *

In this article, we assume that there exist the pseudoscalar $D\bar{D}_{s0}^*(2317)$ and $D^*\bar{D}_{s1}^*(2460)$ molecular states $Z_{1,2}$ and construct the color singlet-singlet molecule-type interpolating currents to study their masses with the QCD sum rules. In calculations, we consider the contributions of the vacuum condensates up to dimension-10 and use the formula $\mu=\sqrt{M_{X/Y/Z}^{2}-(2{\mathbb{M}}_{c})^{2}}$ to determine the energy scales of the QCD spectral densities. The numerical results, $M_{Z_1}=4.61_{-0.08}^{+0.11}\,\text{GeV}$ and $M_{Z_2}=4.60_{-0.06}^{+0.07}\,\text{GeV}$, which lie above the $D\bar{D}_{s0}^*(2317)$ and $D^*\bar{D}_{s1}^*(2460)$ thresholds respectively, indicate that the $D\bar{D}_{s0}^*(2317)$ and $D^*\bar{D}_{s1}^*(2460)$ are difficult to form bound state molecular states, the $Z_{1,2}$ are probably resonance states.     

The rare annihilation decays $\bar{B}^0_{s,d} \to J/\psi\gamma$

We investigate the physics potential of the annihilation decays in the standard model and beyond. In a naive factorization approach, the branching ratios are estimated to be and . In the framework of QCD factorization, we compute the non-factorizable corrections and get , . Future measurements of these decays would be useful for testing the factorization frameworks. The smallness of these decays in the SM makes them sensitive probes of new physics. As an example, we will consider the possible admixture of the (V + A) charge current to the standard (V-A) current. This admixture will give a significant contribution to the decays.Received: 29 August 2003, Revised: 17 January 2004, Published online: 19 March 2004Corresponding author: Y.D. Yang     

Covalent hadronic molecules induced by shared light quarks

After examining Feynman diagrams corresponding to the ${\bar{D}}^{(* )}{{\rm{\Sigma }}}_{c}^{(* )}$, ${\bar{D}}^{(* )}{{\rm{\Lambda }}}_{c}$, ${D}^{(* )}{\bar{K}}^{* }$, and ${D}^{(* )}{\bar{D}}^{(* )}$ hadronic molecular states, we propose a possible binding mechanism induced by shared light quarks. This mechanism is similar to the covalent bond in chemical molecules induced by shared electrons. We use the method of QCD sum rules to calculate its corresponding light-quark-exchange diagrams, and the obtained results indicate a model-independent hypothesis: the light-quark-exchange interaction is attractive when the shared light quarks are totally antisymmetric so they obey the Pauli principle. We build a toy model with four parameters to formulize this picture and estimate binding energies of some possibly-existing covalent hadronic molecules. A unique feature of this picture is that the binding energies of the (I)J^P = (0)1⁺ $D{\bar{B}}^{* }/{D}^{* }\bar{B}$ hadronic molecules are much larger than those of the (I)J^P = (0)1⁺ ${{DD}}^{* }/\bar{B}{\bar{B}}^{* }$ ones, while the (I)J^P = (1/2)1/2⁺ $\bar{D}{{\rm{\Sigma }}}_{c}/\bar{D}{{\rm{\Sigma }}}_{b}/B{{\rm{\Sigma }}}_{c}/B{{\rm{\Sigma }}}_{b}$ hadronic molecules have similar binding energies.     

Role of the Λ(1600) in the ${K}^{-}p \rightarrow {\rm{\Lambda }}{\pi }^{0}{\pi }^{0}$ reaction

Role of the Λ(1600) is studied in the ${K}^{-}p\to {\rm{\Lambda }}{\pi }^{0}{\pi }^{0}$ reaction by using the effective Lagrangian approach near the threshold. We perform a calculation for the total and differential cross sections by considering the contributions from the Λ(1600) and Λ(1670) intermediate resonances decaying into ${\pi }^{0}{{\rm{\Sigma }}}^{* 0}(1385)$ with ${{\rm{\Sigma }}}^{* 0}(1385)$ decaying into ${\pi }^{0}{\rm{\Lambda }}$. Additionally, the non-resonance process from u-channel nucleon pole is also taken into account. With our model parameters, the current experimental data on the total cross sections of the ${K}^{-}p\to {\rm{\Lambda }}{\pi }^{0}{\pi }^{0}$ reaction can be well reproduced. It is shown that we really need the contribution from the Λ(1600) with spin-parity ${J}^{P}=1/{2}^{+}$, and that these measurements can be used to determine some of the properties of the Λ(1600) resonance. Furthermore, we also plot the π⁰Λ invariant mass distributions which could be tested by the future experimental measurements.     

Measurement of A_{FB}^{\mathrm{b}\overline{\mathrm{b}}} in hadronic Z decays using a jet charge technique

The b[`b]\mbox{b}\bar{\mbox{b}} forward-backward asymmetry has been determined from the average charge flow measured in a sample of 3,500,000 hadronic Z decays collected with the DELPHI detector in 1992–1995. The measurement is performed in an enriched b[`b]\mbox{b}\bar{\mbox{b}} sample selected using an impact parameter tag and results in the following values for the b[`b]\mbox{b}\bar{\mbox{b}} forward-backward asymmetry: $ \begin{gathered} A_{FB}^{b\bar b} \left( {89.55 GeV} \right) = 0.068 \pm 0.018 \left( {stat.} \right) \pm 0.0013\left( {syst.} \right) \hfill \\ A_{FB}^{b\bar b} \left( {91.26 GeV} \right) = 0.0982 \pm 0.0047 \left( {stat.} \right) \pm 0.0016\left( {syst.} \right) \hfill \\ A_{FB}^{b\bar b} \left( {92.94 GeV} \right) = 0.123 \pm 0.016 \left( {stat.} \right) \pm 0.0027\left( {syst.} \right) \hfill \\ \end{gathered} $ \begin{gathered} A_{FB}^{b\bar b} \left( {89.55 GeV} \right) = 0.068 \pm 0.018 \left( {stat.} \right) \pm 0.0013\left( {syst.} \right) \hfill \\ A_{FB}^{b\bar b} \left( {91.26 GeV} \right) = 0.0982 \pm 0.0047 \left( {stat.} \right) \pm 0.0016\left( {syst.} \right) \hfill \\ A_{FB}^{b\bar b} \left( {92.94 GeV} \right) = 0.123 \pm 0.016 \left( {stat.} \right) \pm 0.0027\left( {syst.} \right) \hfill \\ \end{gathered} The b[`b]\mbox{b}\bar{\mbox{b}} charge separation required for this analysis is directly measured in the b tagged sample, while the other charge separations are obtained from a fragmentation model precisely calibrated to data. The effective weak mixing angle is deduced from the measurement to be: $ sin^2 \theta _{eff}^1 = 0.23186 \pm 0.00083 $ sin^2 \theta _{eff}^1 = 0.23186 \pm 0.00083      

Three-loop on-shell charge renormalization without integration:\Lambda _{QED}^{\overline {MS} } to four loops

Using algebraic methods, we find the three-loop relation between the bare and physical couplings of one-flavourD-dimensional QED, in terms of Γ functions and a singleF ₃₂ series, whose expansion nearD=4 is obtained, by wreath-product transformations, to the order required for five-loop calculations. Taking the limitD→4, we find that the \(\overline {MS} \) coupling \(\bar \alpha (\mu )\) satisfies the boundary condition $$\begin{gathered} \frac{{\bar \alpha (m)}}{\pi } = \frac{\alpha }{\pi } + \frac{{15}}{{16}}\frac{{\alpha ^3 }}{{\pi ^3 }} + \left\{ {\frac{{11}}{{96}}\zeta (3) - \frac{1}{3}\pi ^2 \log 2} \right. \hfill \\ \left. { + \frac{{23}}{{72}}\pi ^2 - \frac{{4867}}{{5184}}} \right\}\frac{{\alpha ^4 }}{{\pi ^4 }} + \mathcal{O}(\alpha ^5 ), \hfill \\ \end{gathered} $$ wherem is the physical lepton mass and α is the physical fine structure constant. Combining this new result for the finite part of three-loop on-shell charge renormalization with the recently revised four-loop term in the \(\overline {MS} \) β-function, we obtain $$\begin{gathered} \Lambda _{QED}^{\overline {MS} } \approx \frac{{me^{3\pi /2\alpha } }}{{(3\pi /\alpha )^{9/8} }}\left( {1 - \frac{{175}}{{64}}\frac{\alpha }{\pi } + \left\{ { - \frac{{63}}{{64}}\zeta (3)} \right.} \right. \hfill \\ \left. { + \frac{1}{2}\pi ^2 \log 2 - \frac{{23}}{{48}}\pi ^2 + \frac{{492473}}{{73728}}} \right\}\left. {\frac{{\alpha ^2 }}{{\pi ^2 }}} \right), \hfill \\ \end{gathered} $$ at the four-loop level of one-flavour QED.     

Study of the weak annihilation contributions in charmless $$\varvec{B_s\rightarrow VV}$$ decays

In this paper, in order to probe the spectator-scattering and weak annihilation contributions in charmless \(B_s\rightarrow VV\) (where V stands for a light vector meson) decays, we perform the \(\chi ^2\)-analyses for the endpoint parameters within the QCD factorization framework, under the constraints from the measured \(\bar{B}_{s}\rightarrow \) \(\rho ^0\phi \), \(\phi K^{*0}\), \(\phi \phi \) and \(K^{*0}\bar{K}^{*0}\) decays. The fitted results indicate that the endpoint parameters in the factorizable and nonfactorizable annihilation topologies are non-universal, which is also favored by the charmless \(B\rightarrow PP\) and PV (where P stands for a light pseudo-scalar meson) decays observed in previous work. Moreover, the abnormal polarization fractions \(f_{L,\bot }(\bar{B}_{s}\rightarrow K^{*0}\bar{K}^{*0})=(20.1\pm 7.0)\%,(58.4\pm 8.5)\%\) measured by the LHCb collaboration can be reconciled through the weak annihilation corrections. However, the branching ratio of \(\bar{B}_{s}\rightarrow \phi K^{*0}\) decay exhibits a tension between the data and theoretical result, which dominates the contributions to \(\chi _\mathrm{min}^2\) in the fits. Using the fitted endpoint parameters, we update the theoretical results for the charmless \(B_s\rightarrow VV\) decays, which will be further tested by the LHCb and Belle-II experiments in the near future.     

Tau Leptonic Decay τ→lVlVτ in Littlest Higgs Model＊

We consider the τ leptonic decay $\tau\rightarrow l\bar{\nu}_{l}\nu_{\tau}$ in the framework of the littlest Higgs (LH) model and calculate the corrections of new particles to this decay. We find that the contributions of the charged scalars can be safely ignored and the LH model is in perfect agreement with the universality of the couplings of the SU gauge bosons to the leptonic charged currents. The corrections of the LH model to the τ leptonic decay $\tau\rightarrow l\bar{\nu}_{l}\nu_{\tau}$ are not sensitive to the parameter c, but depend strongly on the parameters f and x. The precision measured data about the τ leptonic decay demand that the parameter f approximately equal 3.5 TeV and x>0.1, while agree with the general expectation based on other phenomenological explorations.     

Singularities and accumulation of singularities of πN scattering amplitudes

It is demonstrated that for the isospin I = 1/2 πN scattering amplitude, T^I=1/2(s, t), $s={\left({m}_{N}^{2}-{m}_{\pi }^{2}\right)}^{2}/{m}_{N}^{2}$ and $s={m}_{N}^{2}+2{m}_{\pi }^{2}$ are two accumulation points of poles on the second sheet of complex s plane, and are hence accumulation of singularities of T^I=1/2(s, t). For T^I=3/2(s, t), $s={\left({m}_{N}^{2}-{m}_{\pi }^{2}\right)}^{2}/{m}_{N}^{2}$ is the accumulation point of poles on the second sheet of the complex s plane. The proof is valid up to all orders of chiral expansions.     

Mutually Unbiasedness between Maximally Entangled Bases and Unextendible Maximally Entangled Systems in $\mathbb {C}^{2}\otimes \mathbb {C}^{2^{k}}$

The mutually unbiasedness between a maximally entangled basis (MEB) and an unextendible maximally entangled system (UMES) in the bipartite system \(\mathbb {C}^{2}\otimes \mathbb {C}^{2^{k}} (k>1)\) are introduced and discussed first in this paper. Then two mutually unbiased pairs of a maximally entangled basis and an unextendible maximally entangled system are constructed; lastly, explicit constructions are obtained for mutually unbiased MEB and UMES in \(\mathbb {C}^{2}\otimes \mathbb {C}^{4}\) and \(\mathbb {C}^{2}\otimes \mathbb {C}^{8}\), respectively.     

Study of Z pair production and anomalous couplingsin e + e- collisions at $\sqrt{s}$ between 190 GeV and 209 GeV

A study of Z-boson pair production in e ⁺ e^- annihilation at center-of-mass energies between 190 GeV and 209 GeV is reported. Final states containing only leptons, ( and ), quark and lepton pairs, ( , ) and only hadrons ( ) are considered. In all states with at least one Z boson decaying hadronically, lifetime, lepton and event-shape tags are used to separate pairs from final states. Limits on anomalous ZZ and ZZZ couplings are derived from the measured cross sections and from event kinematics using an optimal observable method. Limits on low scale gravity with large extra dimensions are derived from the cross sections and their dependence on polar angle.Received: 14 July 2003, Published online: 18 December 2003     

Impurity effects of the Λhyperon in the hypernuclear systems ${}_{{\rm{\Lambda }}}^{25}\mathrm{Mg}$ and ${}_{{\rm{\Lambda }}}^{29}\mathrm{Si}$

Based on the beyond-mean-field Skyrme–Hartree–Fock model, impurity effects of the Λhyperon in the hypernuclear systems ${}_{\,{\rm{\Lambda }}}^{25}$ Mg and ${}_{\,{\rm{\Lambda }}}^{29}$ Si are investigated, respectively. Four cases, in which the Λhyperon occupies the single-particle orbitals ${\rm{\Lambda }}$[000]${\tfrac{1}{2}}^{+}$, ${\rm{\Lambda }}$[110]${\tfrac{1}{2}}^{-}$, ${\rm{\Lambda }}$[101]${\tfrac{3}{2}}^{-}$ and ${\rm{\Lambda }}$[101]${\tfrac{1}{2}}^{-}$, are focused. In each case, the potential energy surface and the energy curves projected on certain angular momenta are employed to show the influence of the Λhyperon on the nuclear core. Beside the shrinkage effect that is induced by the Λhyperon occupying the s_Λ orbital, it is found that the Λhyperon on the p_Λ orbital, ${\rm{\Lambda }}$[110]${\tfrac{1}{2}}^{-}$, drives the nuclear core toward a prolate shape, while the ones on the other two p_Λ orbitals, ${\rm{\Lambda }}$[101]${\tfrac{3}{2}}^{-}$ and ${\rm{\Lambda }}$[101]${\tfrac{1}{2}}^{-}$, drive the nuclear core toward an oblate shape. The energy spectra and the corresponding intra-band E2 transition rates for the rotational bands are given as a prediction for future experiments.     

1.5 T下高介电材料几何结构对发射场影响的仿真研究

近年来研究发现,在高场及超高场磁共振成像（MRI）中,高介电材料在提高磁共振射频线圈性能,以及增强图像信噪比方面具有极大的应用潜力.当前高介电材料研究主要集中于其对磁共振图像信噪比的改善,但对于高介电材料几何结构,以及其对发射场分布均匀度影响的研究不多.本研究利用电磁仿真的方法定量分析了1.5 T下,高介电材料几何结构对水模感兴趣区内发射效率均值和发射场$ {B}_{\text{1}}^{\text{+}} $均匀度的影响.结果表明,高介电材料的几何结构对$ {B}_{\text{1}}^{\text{+}} $均匀度会产生较大影响;比较了不同几何结构的高介电衬垫之后发现,加入四等分圆筒状高介电衬垫后,感兴趣区内发射效率提升最高,同时$ {B}_{\text{1}}^{\text{+}} $均匀度也保持良好.该结果对高介电材料应用于MRI具有重要的参考价值.